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Sensi: Difference between revisions

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→Tunings: + norm-based & target tunings
m Adopt CWE tuning. Cleanup
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{| class="wikitable right-1 right-2 sortable"
{| class="wikitable right-1 right-2 sortable"
|-
|-
! #
! #
! Cents*
! Cents*
! class="unsortable" | Approximate ratios**
! class="unsortable" | Approximate ratios
|-
|-
| 0
| 0
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|-
|-
| 1
| 1
| 443.3
| 443.4
| 9/7, 13/10
| 9/7, 13/10
|-
|-
| 2
| 2
| 886.6
| 886.7
| 5/3, 42/25
| 5/3, 42/25
|-
|-
| 3
| 3
| 129.9
| 130.1
| 13/12, 14/13, 15/14, 27/25
| 13/12, 14/13, 15/14, 27/25
|-
|-
| 4
| 4
| 573.3
| 573.4
| 7/5, 18/13, 25/18
| 7/5, 18/13, 25/18
|-
|-
| 5
| 5
| 1016.6
| 1016.8
| 9/5
| 9/5
|-
|-
| 6
| 6
| 259.9
| 260.1
| 7/6, 15/13
| 7/6, 15/13
|-
|-
| 7
| 7
| 703.2
| 703.5
| '''3/2'''
| '''3/2'''
|-
|-
| 8
| 8
| 1146.5
| 1146.9
| 27/14, 35/18
| 27/14, 35/18
|-
|-
| 9
| 9
| 389.8
| 390.2
| '''5/4'''
| '''5/4'''
|-
|-
| 10
| 10
| 833.2
| 833.6
| '''13/8''', 21/13
| '''13/8''', 21/13
|-
|-
| 11
| 11
| 76.5
| 76.9
| 21/20, 25/24
| 21/20, 25/24
|-
|-
| 12
| 12
| 519.8
| 520.3
| 27/20
| 27/20
|-
|-
| 13
| 13
| 963.1
| 963.7
| '''7/4'''
| '''7/4'''
|-
|-
| 14
| 14
| 206.4
| 207.0
| '''9/8'''
| '''9/8'''
|-
|-
| 15
| 15
| 649.7
| 650.4
| 35/24 (sensor '''16/11''', sensus 22/15)
| 35/24 (sensor '''16/11''', sensus 22/15)
|-
|-
| 16
| 16
| 1093.1
| 1093.7
| '''15/8''' (sensor '''32/17''', sensus 17/9)
| '''15/8''' (sensor '''32/17''', sensus 17/9)
|-
|-
| 17
| 17
| 336.4
| 337.1
| 39/32 (sensus 17/14)
| 39/32 (sensus 17/14)
|-
|-
| 18
| 18
| 779.7
| 780.4
| 25/16
| 25/16
|-
|-
| 19
| 19
| 23.0
| 23.8
| 49/48, 65/64, 81/80
| 49/48, 65/64, 81/80
|-
|-
| 20
| 20
| 466.3
| 467.2
| '''21/16'''
| '''21/16'''
|}
|}
<nowiki/>* In 2.3.5.7.13 CTE tuning
<nowiki/>* In 2.3.5.7.13 CWE tuning
 
<nowiki/>** 2.3.5.7.13 ratio interpretations


=== In Sensi[8] ===
=== In Sensi[8] ===
Sensi[8] is a [[mos scale]] with a [[3L&nbsp;5s]] pattern (or [[5L&nbsp;3s]] in extreme cases where the generator is larger than 450{{c}}). See [[3L&nbsp;5s#Modes]] (resp. [[5L&nbsp;3s#Modes]]) to see which modes have which qualities for each interval size.
Sensi[8] is a [[mos scale]] with a [[3L&nbsp;5s]] pattern (or [[5L&nbsp;3s]] in extreme cases where the generator is larger than 450{{c}}). See [[3L&nbsp;5s #Modes]] (resp. [[5L&nbsp;3s #Modes]]) to see which modes have which qualities for each interval size.


Sortable table of Sensi[8]'s major and minor intervals in various sensi tunings:
Sortable table of Sensi[8]'s major and minor intervals in various sensi tunings:
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{{Main| Chords of sensus }}
{{Main| Chords of sensus }}


The "fundamental" otonal consonance of sensi (in this article's definition of sensi) is 4:5:6:7:9:13. However, the full chord isn't available in the 8-note MOS.
The fundamental otonal consonance of sensi is 4:5:6:7:9:13. However, the full chord is only available in the 19-note mos.


One of the most common consonant triads in sensi is the 6:10:13 triad, which spans 3 generators. Sensi[8] has five 6:10:13 triads, four 7:9:13 triads, three 5:6:7:9 tetrads and one 5:6:7:9:13 pentad. Having many diminished triads, it is similar to the 12edo diminished scale in some ways. Sensi is interesting mainly because it gives new 13-limit interpretations to fairly familiar (in the sense of extended meantone-like) intervals. Restricted to the 8-note MOS, it is essentially a [[non-over-1 temperament]].
One of the most common consonant triads in sensi is the 6:10:13 triad, which spans 3 generators. Sensi[8] has five 6:10:13 triads, four 7:9:13 triads, three 5:6:7:9 tetrads and one 5:6:7:9:13 pentad. Having many diminished triads, it is similar to the 12edo diminished scale in some ways. Sensi is interesting mainly because it gives new 13-limit interpretations to fairly familiar (in the sense of extended meantone-like) intervals. Restricted to the 8-note MOS, it is essentially a [[non-over-1 temperament]].


Melodically, sensi[8] sounds fairly familiar because many intervals are either 5-limit or have familiar categorical interpretations, being represented in the meantone tuning [[19edo]]. For example, the small step of about 130{{c}} categorizes pretty well as a large semitone (except at places in the scale where two of them make a flat subminor third); the large step is a small whole tone representing 10/9.
Melodically, Sensi[8] sounds fairly familiar because many intervals are either 5-limit or have familiar categorical interpretations, being represented in the meantone tuning [[19edo]]. For example, the small step of about 130{{c}} categorizes pretty well as a large semitone (except at places in the scale where two of them make a flat subminor third); the large step is a small whole tone representing 10/9.


The root-sen5th-sen8th chords in sensi[8] usually spell 5:7:9 (root-minor sen5th-minor sen8th) and 7:10:13 (root-major sen5th-major sen8th) chords (shown in the Anti-Dylathian mode QJKLMNOPQ = ssLssLsL):
The root-sen5th-sen8th chords in Sensi[8] usually spell 5:7:9 (root-minor sen5th-minor sen8th) and 7:10:13 (root-major sen5th-major sen8th) chords (shown in the Anti-Dylathian mode QJKLMNOPQ = ssLssLsL):
* Q M P = ssLs sLs L ≈ 5:7:9
* Q M P = ssLs sLs L ≈ 5:7:9
* J N Q = sLss LsL s is the odd one out
* J N Q = sLss LsL s is the odd one out
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* P L O = LssL ssL s ≈ 7:10:13
* P L O = LssL ssL s ≈ 7:10:13


Other otonal chords approximated in the 8-note MOS include:
Other otonal chords approximated in the 8-note mos include:


* {{dash|Root, maj. sen7th, maj. sen8th ≈ 7:12:13|s=space}}
* {{dash|Root, maj. sen7th, maj. sen8th ≈ 7:12:13|s=space}}
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== Visualizations ==
== Visualizations ==
=== Steps of sensi ===
=== Steps of sensi ===
This diagram shows sensi[5], [8], [11], and [19] with intervals named in relation to the L and s of sensi[8].  
This diagram shows Sensi[5], [8], [11], and [19] with intervals named in relation to the L and s of Sensi[8].  


[[File:steps_of_sensi.png|Steps of sensi|alt=steps_of_sensi.png]]
[[File:steps_of_sensi.png|Steps of sensi|alt=steps_of_sensi.png]]
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=== Map of sensi ===
=== Map of sensi ===
These diagrams relate the sensi generator chain (horizontal axis) to the steps within the octave (vertical axis) for sensi[8] and [11].  
These diagrams relate the sensi generator chain (horizontal axis) to the steps within the octave (vertical axis) for Sensi[8] and [11].  


[[File:map_of_sensi-8-.png|Map of sensi[8]|alt=map_of_sensi[8].png]]
[[File:map_of_sensi-8-.png|Map of Sensi[8]|alt=map_of_sensi[8].png]]
[[File:map_of_sensi-11-_correction2.png|map of sensi[11]|alt=map_of_sensi[11]_correction2.png]]
[[File:map_of_sensi-11-_correction2.png|Map of Sensi[11]|alt=map_of_sensi[11]_correction2.png]]


=== Isomorphic layout ===
=== Isomorphic layout ===
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